How can I associate a vehicle with the lowest total distance traveled to the longest route, and the one with the longest cumulated route to the shortest route. This is to try to make all vehicles have balanced distances a month.

If I understand correctly, your problem is that, for each vehicle, there is an associated total distance traveled (termed as L), which is the accumulated distance the vehicle has traveled in previous runs (days), and what you want is that the vehicle with larger L should be doing a shorter route in the current run (day).

If so, I think what you can try is to set a separate vehicle type for each vehicle and set the cost per distance parameter for each vehicle type according to the value of L - the larger L is, the larger the cost per distance parameter should be, so that the vehicle is encouraged to do a shorter route.